Overlap as function of distance

[ftft]

I am trying to find a way to calculate the overlap integral between atomic orbitals centred on two different atoms, A & B as a function of the separation distance. I hope someone in the forum can give a hint on how to do that.
Thanks,
ftft

 

[Khashishi]

Since orbitals are normally written in spherical polar coordinates, you'll have to convert them into Cartesian coordinates. I assume you know the equations for the spherical harmonics and the radial wavefunction. But the orbitals also get distorted by the presence of the other atom, so it becomes hard.

 

[ftft]

That's a good point Khashishi..
OK.. what if we generalize the problem to two molecules, A & B? each will then have molecular orbitals made by LCAO. To measure overlap in this case: Do we use the Slater wave function (which is determinant of LCAOs including occupied and empty orbitals) for each molecule? Or is it enough to compose the wave function from occupied orbitals? Mathematically, is it enough to calculate the inner product of the two (chosen) wave functions? I am assuming that only those parts of the two wave functions which see each other will contribute to the overlap integral.. how mathematically can we restrict the overlap a small part of the wave functions?